# FIND SLOPE OF THE TANGENT TO THE CURVE AT THE POINT WORKSHEET

Use the first derivative to find the slope of the tangent line to the given curve at the given point:

Problem 1 :

y = 2x2 + 6 at (-1, 8)

Solution

Problem 2 :

y = -x2 + 2x - 3 at (2, 3)

Solution

Problem 3 :

y = 4 - 3x3 at (1, 1)

Solution

Problem 4 :

Solution

Problem 5 :

Tangent lines are drawn to the parabola

y = x2 at (2, 4) and (-1/8, 1/64)

Prove the tangents are perpendicular.

Solution

Problem 6 :

Find a point on the parabola

y = -x2 +3x + 4

where the slope of the tangent line is 5.

Solution

Problem 7 :

Find the slope of the tangent line to the graph of

3x2 + 5 lny = 12 at (2, 1) is

A)  -12/5      B)  12/5        C)  5/12       D)  12      E)  -7

Solution

Problem 8 :

Solution

1)  2

2)  0

3)  -5

4)  8

5)  So, the tangents drawn at the points (2, 4) and (-1/8, 1/64) for the parabola, they are perpendicular.

6)   the required point is (-1, 0).

7)  the required slope is -12/5. Option A.

8)  the required value of y is 58/7, option C.

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